Find the indefinite integral.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^5{e}^{x^5-6}dx$

a$.e^{x^6-6}+c$

b$.-\frac{1}{2}x+c$

c$.\frac{1}{6}{e}^{x^6-6}+c$

d$.\frac{1}{6}ln(x^6-6)+C$